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A Targeted Maximum Likelihood Estimator for Two-Stage Designs

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  • Rose Sherri

    (University of California, Berkeley)

  • van der Laan Mark J.

    (University of California, Berkeley)

Abstract

We consider two-stage sampling designs, including so-called nested case control studies, where one takes a random sample from a target population and completes measurements on each subject in the first stage. The second stage involves drawing a subsample from the original sample, collecting additional data on the subsample. This data structure can be viewed as a missing data structure on the full-data structure collected in the second-stage of the study. Methods for analyzing two-stage designs include parametric maximum likelihood estimation and estimating equation methodology. We propose an inverse probability of censoring weighted targeted maximum likelihood estimator (IPCW-TMLE) in two-stage sampling designs and present simulation studies featuring this estimator.

Suggested Citation

  • Rose Sherri & van der Laan Mark J., 2011. "A Targeted Maximum Likelihood Estimator for Two-Stage Designs," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-21, March.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:17
    DOI: 10.2202/1557-4679.1217
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    References listed on IDEAS

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    1. Stitelman Ori M & van der Laan Mark J., 2010. "Collaborative Targeted Maximum Likelihood for Time to Event Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-46, June.
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    3. Weiwei Wang & Daniel Scharfstein & Zhiqiang Tan & Ellen J. MacKenzie, 2009. "Causal inference in outcome‐dependent two‐phase sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 947-969, November.
    4. E. Vittinghoff & D. C. Bauer, 2006. "Case-Only Analysis of Treatment–Covariate Interactions in Clinical Trials," Biometrics, The International Biometric Society, vol. 62(3), pages 769-776, September.
    5. van der Laan Mark J. & Gruber Susan, 2010. "Collaborative Double Robust Targeted Maximum Likelihood Estimation," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-71, May.
    6. van der Laan Mark J. & Polley Eric C & Hubbard Alan E., 2007. "Super Learner," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-23, September.
    7. Gruber Susan & van der Laan Mark J., 2010. "A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-18, August.
    8. Rose Sherri & van der Laan Mark J., 2008. "Simple Optimal Weighting of Cases and Controls in Case-Control Studies," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-24, September.
    9. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    10. Rosenblum Michael & van der Laan Mark J., 2010. "Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-30, April.
    11. Rose Sherri & van der Laan Mark J., 2009. "Why Match? Investigating Matched Case-Control Study Designs with Causal Effect Estimation," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-26, January.
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    Cited by:

    1. Gilbert Peter B. & Blette Bryan S. & Hudgens Michael G. & Shepherd Bryan E., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    2. van der Laan Mark J. & Gruber Susan, 2012. "Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-41, May.
    3. Gilbert Peter B. & Blette Bryan S. & Hudgens Michael G. & Shepherd Bryan E., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    4. Nima S. Hejazi & Mark J. van der Laan & Holly E. Janes & Peter B. Gilbert & David C. Benkeser, 2021. "Efficient nonparametric inference on the effects of stochastic interventions under two‐phase sampling, with applications to vaccine efficacy trials," Biometrics, The International Biometric Society, vol. 77(4), pages 1241-1253, December.
    5. Sherri Rose & Julie Shi & Thomas G. McGuire & Sharon-Lise T. Normand, 2017. "Matching and Imputation Methods for Risk Adjustment in the Health Insurance Marketplaces," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 525-542, December.
    6. Paul S. Albert & Aiyi Liu & Tonja Nansel, 2014. "Efficient logistic regression designs under an imperfect population identifier," Biometrics, The International Biometric Society, vol. 70(1), pages 175-184, March.

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